Jahiliyyah is a technical term coined by Muslim historians and thinkers to refer to the time before the advent of Islam. In other words, anything occurring before the year 610 CE would be considered from the jahiliyya time. Arabic poetry before that year is often referred to as jahiliyya poetry.
The concept is derived from the root ja-ha-la, which has to do with knowing and not knowing. In that sense, jahiliyya can be understood to refer to the time before Islamic Enlightenment, to borrow the Western concept associated with the Age of Reason. Muslim thinks coined the "Age of Ignorance", for similar purposes.
Islamists like Qotb, would consider Jahiliyya anytime where Muslims are ruled by non-Islamic government.
It helps to remember that the concept, as is the case often, is a political statement more than a factual one.